We consider the inverse problem to determine the shape of an insulated inclusion within a heat conducting medium from overdetermined Cauchy data of solutions for the heat equation on the accessible exterior boundary of the medium. For the approximate solution of this ill-posed and nonlinear problem we propose a regularized Newton iteration scheme based on a… (More)
In this paper we describe a fully discrete quadrature method for the numerical solution of a hypersingular integral equation of the rst kind for the scattering of time-harmonic elastic waves by a cavity crack. We establish convergence of the method and prove error estimates in a HH older space setting. Numerical examples illustrate the convergence results.